This invention relates generally to the field of post-processing of images, such as trabecular bone images, obtained by MRI, CT, or other image technologies to increase apparent image resolution without partial volume blurring for structural dimensions in which image voxel size is larger than the typical structural element to be resolved, and to the use of these parameters to determine trabecular network strength as a risk factor in the assessment of osteoporosis.
Magnetic Resonance Imaging (MRI) is a powerful tool for noninvasively quantifying tissue morphology. However, when voxel size is larger than the structures of interest, partial volume blurring complicates accurate measurement of structural parameters. On the other hand, acquisition of images at higher resolution often exacts an unacceptable signal-to-noise penalty, and thus, does not represent a viable alternative. For example, these constraints have been the major obstacle to the development of MRI as a means of quantifying trabecular bone architecture in vivo for the purpose of predicting fracture risk in osteopenic subjects (Link et al., J. Bone Miner. Res. 13:1175-1182 (1998); Wehrli et al., Radiology 206:347-357 (1998); Majumdar et al., J. Bone Miner. Res. 12:111-118 (1997); Gordon et al., Med. Phys. 24:585-593 (1997)).
Trabecular bone (TB) (also known as cancellous bone), which makes up most of the axial skeleton and ends near the joints of the long bones, consists of a lattice of interconnected plates and rods that confer mechanical strength to the skeleton at minimum weight. However, there is growing evidence that in addition to the volume fraction of the bone (often quantified in terms of bone density), the three-dimensional (3D) arrangement of the trabecular network is a major determinant of elastic modulus and ultimate strength.
In general, characterization of the strength of trabecular lattices from three-dimensional (3D) images can be divided into three major categories: material, scale and topology (DeHoff et al., J. Microscopy 95:69-91 (1972)). xe2x80x98Material propertiesxe2x80x99 describe the bone material; xe2x80x98scale propertiesxe2x80x99 describe the size and thickness (local volume properties) of the trabecular elements; and the xe2x80x98topological propertiesxe2x80x99 describe the spatial arrangement of the bone material in the network. These parameters change characteristically with subject age.
A common diagnostic screening method for osteoporosis is based on xe2x80x98dual-energy X-ray absorptiometryxe2x80x99 (DEXA) (Wahner et al., The Evaluation of Osteoporosis: Dual Energy X-Ray Absorptiometry in Clinical Practice, Cambridge: University Press, 1994) to measure integral bone mineral density (BMD). This method, however, does not distinguish between trabecular and cortical bone and ignores the role of structure as a contributor to mechanical competence.
Since trabecular thickness (80-150 xcexcm) is typically less than the achievable voxel size in vivo (xcx9c150 xcexcm), accurate structural information is difficult to obtain. The common approach toward quantifying trabecular structure has been to classify voxels as either xe2x80x9cbonexe2x80x9d or xe2x80x9cmarrowxe2x80x9d via binary segmentation. In the low spatial-resolution regime, however, the xe2x80x9cbonexe2x80x9d voxels contain varying amounts of bone, usually with a higher proportion of marrow. Therefore, to avoid the loss of information inherent in binary classification, a means of estimating the bone volume fraction (BVF) in each voxel (Hwang et al., Int. J Imaging Syst. Technol. 10:186-198 (1999)) was devised, referred to as BVF mapping. Linear interpolation has commonly been applied to increase the apparent resolution of digital images. In one dimension, for example, BVF at a spatial location between the centers of two adjacent voxels would be computed as the average of the two voxels. As a result, additional values calculated in this manner can never increase beyond the original values, and thus, contradict the axiom that smaller voxels are more likely to contain larger fractions of bone.
Clearly, there remains a need in the art to increase the apparent resolution of the BVF map, and to overcome the partial volume blurring which presently precludes accurate measurement of structural dimensions in the limited-resolution regime in which image voxel size is larger than the typical structural element to be resolved. Since acquiring images at increased resolution often exacts an unacceptable signal-to-noise penalty, methods to alleviate the adverse effects of partial volume blurring are instrumental for the accurate measurement of architectural parameters in applications, such as predicting the mechanical competence of trabecular bone networks. Once they have been accurately measured, parameters for quantifying the visible differences in architecture have recently been derived and applied to predict fracture risk (Wehrli et al., J. Bone Miner. Res. (2001) in press).
Prior to the present invention, even with the most advanced technology, it has not been possible to obtain images of trabecular architecture in vivo at a resolution better than trabecular thickness. In the distal radius, voxel sizes reported by MR range from 5.5xc3x9710xe2x88x923 mm3 (Song et al, Magn. Reson. Med. 41:947-953 (1999)) to 12xc3x9710xe2x88x923 mm3(Majumdar et al., 1997), corresponding to a mean linear resolution of 187 and 257 xcexcm, respectively. In peripheral quantitative computed tomography (p-QCT) of the wrist, the smallest reported voxel size is 160 xcexcm (Laib et al., Technol. Health Care 6:329-337 (1998)). However, the point-spread function is considerably wider in CT than in MR, resulting in an effective resolution closer to 300 xcexcm. Realizing the limitations of image resolution, Majumdar et al., 1997 refer to the derived histomorphometric measures as xe2x80x9capparent.xe2x80x9d Mxc3xcller et al. demonstrated excellent serial reproducibility in histomorphometric parameters obtained in vivo in the distal radius of test subjects by p-QCT (Mxc3xcller et al., J. Bone Miner. Res. 11: 1745-1750 (1996)), even though the reported trabecular thickness values were overestimated by at least a factor of 2. While apparent histomorphometric measures may still be useful as long as they track true variations in these parameters, analytical approaches aimed at deriving topological parameters (Pothuaud et al., J. Microse. 199:149-161 (2000); Saha et al., Int. J. Imaging Sys. Technol. 11:81-90 (2000); Gomberg et al., IEEE Trans. Med. Imaging 19:166-174 (2000); Hildebrand et al, J. Bone Miner. Res. 14:1167-1174 (1999)) are unlikely to yield meaningful parameters at in vivo resolution without enhancement of the apparent resolution.
The present invention comprises a novel image post-processing method, system and device for increasing apparent image resolution of images, such as trabecular bone images, obtained by MRI, CT, or other image technologies. Referred to as xe2x80x9csubvoxel processing,xe2x80x9d the method and system are applicable to volumes of interest containing material phases of two discrete signal intensities.
The accuracy of the method has been demonstrated by nonlimiting example, using a micro-computed tomography (xcexc-CT) image of human trabecular bone, to show that subvoxel processing is significantly more accurate than trilinear interpolation in decreasing apparent voxel size, especially in the presence of noise. In addition, the effectiveness of the method has been illustrated with MR images of human trabecular bone acquired in vivo, although it is also applicable ex vivo. The subvoxel-processed images were shown to have architectural features characteristic of images acquired at higher spatial resolution.
In a preferred embodiment of the invention, the method is illustrated with images of trabecular bone; however, the algorithm may easily be applied to images of other materials, which may be considered to locally contain only two phases. The method of Bayesian subvoxel classification (Wu et al., Magn. Reson. Med. 31:302-308 (1994)) also divides voxels into subvoxels; however in contrast to a preferred embodiment of the present invention, the Bayesian method produces its output as a binarized image, i.e., the subvoxels are constrained to contain either 100% bone or 100% marrow. By comparison, subvoxel processing of the preferred embodiment of the present invention assigns partial fractions to each subvoxel (Hwang et al., Proc. Internat""l Soc. Magnetic Resonance Med., Denver, 2000, p. 2134, herein incorporated by reference).
A preferred embodiment of the invention provides a method to increase apparent image resolution by post-processing an image of a volume comprising material phases having at least two discrete signal intensities, wherein the method comprises: algorithmically subdividing each voxel of the image into subvoxels; assigning voxel intensities (weights) to each subvoxel computed on the basis of local neighborhood criteria and strict mass conservation; and automatically computing a resolution-enhanced image by retaining the original spatial locations of the subvoxels, which have been sorted in terms of assigned weights.
Another preferred embodiment of the invention provides a system to increase apparent image resolution by post-processing an image of a volume comprising material phases having at least two discrete signal intensities, wherein the system comprises: at least one means for algorithmically subdividing each voxel of the image into subvoxels; at least one means for assigning voxel intensities (weights) to each subvoxel computed on the basis of local neighborhood criteria and strict mass conservation; and at least one means for automatically computing a resolution-enhanced image by retaining the original spatial locations of the subvoxels, which have been sorted in terms of assigned weights.
Yet another preferred embodiment of the invention provides a device to increase apparent image resolution by post-processing an image of a volume comprising material phases having at least two discrete signal intensities, wherein the device comprises: a computer-readable signal-bearing medium; at least one means in the medium for algorithmically subdividing each voxel of the image into subvoxels; at least one means in the medium for assigning voxel intensities (weights) to each subvoxel computed on the basis of local neighborhood criteria and strict mass conservation; and at least one means in the medium for automatically computing a resolution-enhanced image by retaining the original spatial locations of the subvoxels, which have been sorted in terms of assigned weights.
In each preferred embodiment, the images may be obtained by any known imaging process, including, for example, MRI, CT, ultrasound, nuclear imaging, included emission tomography modalities, microscopy (light or electron), photography, x-ray projection and optical digital imaging.
Moreover, it is provided an embodiment in which subdividing each voxel further comprises subdividing each voxel into eight subvoxels by strictly enforcing conservation of bone mass, such that total solid volume fraction in the original voxel is divided among the subvoxels on a weighted basis, and subvoxels are sorted in order of decreasing weight. A subvoxel is determined by the amount and location of solid outside the voxel, but adjacent to the subvoxel; and wherein the weight for each subvoxel is computed as the sum of the voxels adjacent to that subvoxel. Blurring of the image is eliminated by a repeated algorithmic process, comprising classifying each subvoxel as a boundary subvoxel or a central subvoxel, based upon output of the original weighting determination, wherein (i) solid-containing subvoxels are classified as boundary or central subvoxels on the basis of adjacency and connectivity criteria; (ii) boundary subvoxels are not assigned a solid weight until the central voxels contain 100% solid; (iii) central subvoxels are filled with solid by assigning primary and secondary weights, wherein solid is partitioned among the subvoxels on the basis of the primary weights; and (iv) boundary subvoxels are similarly filled based upon secondary weights, but the primary weights are set to zero.
It is further provided in a preferred embodiment that the subvoxels may be further sorted in order of decreasing primary weights, and yet further sorted within the same primary weight in order of decreasing secondary weights.
Additional objects, advantages and novel features of the invention will be set forth in part in the description, examples and figures which follow, and in part will become apparent to those skilled in the art on examination of the following, or may be learned by practice of the invention.